ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3eqtr2ri Unicode version

Theorem 3eqtr2ri 2167
Description: An inference from three chained equalities. (Contributed by NM, 3-Aug-2006.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Hypotheses
Ref Expression
3eqtr2i.1  |-  A  =  B
3eqtr2i.2  |-  C  =  B
3eqtr2i.3  |-  C  =  D
Assertion
Ref Expression
3eqtr2ri  |-  D  =  A

Proof of Theorem 3eqtr2ri
StepHypRef Expression
1 3eqtr2i.1 . . 3  |-  A  =  B
2 3eqtr2i.2 . . 3  |-  C  =  B
31, 2eqtr4i 2163 . 2  |-  A  =  C
4 3eqtr2i.3 . 2  |-  C  =  D
53, 4eqtr2i 2161 1  |-  D  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1331
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-4 1487  ax-17 1506  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-cleq 2132
This theorem is referenced by:  funimacnv  5199  uniqs  6487  ef01bndlem  11474  cos2bnd  11478  sinhalfpilem  12894
  Copyright terms: Public domain W3C validator